Problem: Gabriela is 8 years younger than Daniel. For the last two years, Daniel and Gabriela have been going to the same school. Ten years ago, Daniel was 5 times as old as Gabriela. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Gabriela. Let Daniel's current age be $d$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $d = g + 8$ Ten years ago, Daniel was $d - 10$ years old, and Gabriela was $g - 10$ years old. The information in the second sentence can be expressed in the following equation: $d - 10 = 5(g - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = d - 8$ . Substituting this into our second equation, we get the equation: $d - 10 = 5($ $(d - 8)$ $ -$ $ 10)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 10 = 5d - 90$ Solving for $d$ , we get: $4 d = 80$ $d = 20$.